Set Species

class sage.combinat.species.set_species.SetSpecies(min=None, max=None, weight=None)

Bases: GenericCombinatorialSpecies, UniqueRepresentation

Returns the species of sets.

EXAMPLES:

sage: E = species.SetSpecies()
sage: E.structures([1,2,3]).list()
[{1, 2, 3}]
sage: E.isotype_generating_series()[0:4]
[1, 1, 1, 1]

sage: S = species.SetSpecies()
sage: c = S.generating_series()[0:3]
sage: S._check()
True
sage: S == loads(dumps(S))
True

class sage.combinat.species.set_species.SetSpeciesStructure(parent, labels, list)

Bases: GenericSpeciesStructure

automorphism_group()

Returns the group of permutations whose action on this set leave it fixed. For the species of sets, there is only one isomorphism class, so every permutation is in its automorphism group.

EXAMPLES:

sage: F = species.SetSpecies()
sage: a = F.structures(["a", "b", "c"]).random_element(); a
{'a', 'b', 'c'}
sage: a.automorphism_group()                                                # needs sage.groups
Symmetric group of order 3! as a permutation group

canonical_label()

EXAMPLES:

sage: S = species.SetSpecies()
sage: a = S.structures(["a","b","c"]).random_element(); a
{'a', 'b', 'c'}
sage: a.canonical_label()
{'a', 'b', 'c'}

transport(perm)

Returns the transport of this set along the permutation perm.

EXAMPLES:

sage: F = species.SetSpecies()
sage: a = F.structures(["a", "b", "c"]).random_element(); a
{'a', 'b', 'c'}
sage: p = PermutationGroupElement((1,2))                                    # needs sage.groups
sage: a.transport(p)                                                        # needs sage.groups
{'a', 'b', 'c'}

sage.combinat.species.set_species.SetSpecies_class

alias of SetSpecies